Computer-based data analysis is a significant driver in today's economy. For example, various machine learning techniques and algorithms, e.g., deep learning and neural network algorithms, may attempt to process or analyze data and identify or derive useful information, relationships, and/or conclusions about the data being analyzed. In this example, by identifying or deriving information about input data, such machine learning techniques and algorithms may be deployed to solve or handle numerous applications (e.g., playing Go, chess, or other games, medical diagnosis, and/or autonomous driving).
In various applications or uses, computer-based data analysis may use detected or assumed relationships between input data or variables. For example, computer-based data analysis may attempt to detect dependence (or a related dependence structure) between a given set of variables. One significant achievement in detecting dependence between variables occurred in the 1880s when Francis Galton introduced a statistical method known as linear regression to study if two variables are linearly associated. This line of inquiry gave rise to a well-known statistic, the Pearson correlation coefficient, which quantifies a linear association between variables. Although widely used in various applications, the linearity assumption is problematic, particularly limiting in the complex, exploratory “Big Data” era when the dependence between variables can be arbitrary (e.g., non-linear). Consequently, there has been a dramatic increase in researching techniques for identifying non-linear dependence between variables.